Michael P. Spathopoulos

Pendulation control of an offshore crane

This paper considers a control system for a crane that reduces pendulation of suspended loads in offshore lifting operations. The modelling of the ship crane is studied and an anti-pendulation arm is designed and proposed. Two different types of models are derived, one based on torque and one kinematic. For the torque model, Lyapunov analysis and non-linear control design is applied on the vertical plane. Linear control design techniques for the linearized kinematic model are applied in both vertical and horizontal planes. These techniques are based on linear quadratic Gaussian (LQG) and generalized predictive control (GPC). The advantage for the linear control designs is the explicit use of the vessel dynamics and sea wave disturbances in the control design that considerably improves the controlled pendulation of the crane. Design issues, simulation results and comparison studies are considered.

Supervisory target control for hybrid systems

The problem of systematically synthesizing supervisory control laws that satisfy eventuality and efficiency requirements for hybrid systems modelled by hybrid automata is considered. Here, the efficiency requirement is specified by weighting the discrete transitions of the system. The optimization of the efficiency requirement is considered in the min-max sense due to the existence of disturbance inputs. Adopting a game theoretic approach, the high priority eventuality requirement is considered first and the class of controls, in which the low priority efficiency requirement should be optimized, is obtained. Then, a dynamic programming algorithm, which determines the value function of the optimization problem, is derived. A synthesis problem on a simplified batch process plant is considered to illustrate a potential application of the approach.

Hybrid control synthesis for eventuality specifications using level set methods

This paper is concerned with the extraction of controllers for hybrid systems with respect to eventuality specifications. Given a hybrid system modelled by a hybrid automaton and a target set of states, the objective is to compute the maximal set of initial states together with the hybrid control policy such that all the trajectories of the controlled system reach the target in finite time. Due to the existence of set-valued disturbance inputs, the problem is studied in a game-theoretic framework. Having shown that a least restrictive solution does not exist, we propose a dynamic programming algorithm that computes the maximal initial set and a controller with the desired property. To implement the algorithm, reachable sets of pursuit-evasion differential games need to be computed. For that reason level set methods are employed, where the boundary of the reachable set is characterized as the zero level set of a Hamilton–Jacobi equation. The procedure for the numerical extraction of the controller is presented in detail and examples illustrate the methodology. Finally, to demonstrate the practical character of our results, a control design problem in the benchmark system of the batch evaporator is considered as an eventuality synthesis problem and solved using the proposed methodology.

A state-set estimation algorithm for linear systems in the presence of bounded disturbances

This paper concerns the problem of state-set estimation for discrete-time linear systems. The linear system is given in state-space form and the systems uncertainty is described by bounded scalar variations. We present a recursive algorithmic procedure of computing guaranteed estimated state sets. In particular, a polyhedron variation algorithm is presented. The new algorithm is based on linear-programming and sensitivity analysis techniques for improved computational efficiency and practicability.

Supervisory control for rectangular hybrid automata

We consider the problem of supervisory control for compact rectangular automata with uniform rectangular activity, i.e. initialised. The supervisory controller is state feedback and can disable only discrete-event transitions in order to solve the non-blocking forbidden state problem. The non-blocking problem is defined under both strong and weak conditions. For the latter maximally permissive solutions that are computable on a finite quotient space characterised by language equivalence are derived.

Eventuality synthesis for controlled linear automata

The synthesis of hybrid controllers that satisfy eventuality specifications is studied. Linear automata that accept continuous inputs are considered. The feedback control derivation is based on reachability analysis. A computational procedure for the reachable set, based on Fourier elimination and convexity analysis techniques, is derived. A feedback controller that guarantees the system will visit a given convex target set without violating state constraints is obtained.

A pendulation control system for offshore lifting operations

Abstract This paper presents a control system that reduces pendulation of suspended loads in offshore lifting operations. The kinematic model of the ship and crane together with the designed anti-pendulation ami are presented. Linear control design techniques for the linearised model are proposed aiming at controlling pendulation in the presence of sea disturbances. These techniques involve LGQ and Generalised predictive control. The use of a dynamic model for the vessel dynamics and the sea wave disturbances in the control design improve the behaviour of the controlled system. Finally simulation results and comparisons are given.

Time optimal control systhesis for discrete time hybrid automata

In this paper, the problem of time-optimal control for hybrid systems with discrete-time dynamics is considered. The hybrid controller steers all trajectories starting from a maximal set to a given target set in minimum time. We derive an algorithm that computes this maximal winning set. Also, algorithms for the computation of level sets associated with the value function rather than the value function itself are presented. We show that by solving the reachability problem for the discrete time hybrid automata we obtain the time optimal solution as well. The control synthesis is subject to hard constraints on both control inputs and states. For linear discrete-time dynamics, linear programming and quantifier elimination techniques are employed for the backward reachability analysis. Emphasis is given on the computation of operators for non-convex sets using an extended convex hull approach. A two-tank example is considered in order to demonstrate the techniques of the paper.

Supervisory eventuality synthesis

This paper presents a study on the eventuality synthesis problem for hybrid automata. Given a hybrid automaton and a target set of states, we seek to compute a feedback controller as well as the maximal set of initial states from which all the trajectories of the closed system eventually reach the target set. Considering control action on the discrete event level only and applying reachability analysis, we derive a feedback eventuality controller Since, generally, there does not exist a least restrictive eventuality controller we propose a second controller and derive the necessary condition under which it becomes the least restrictive eventuality controller Finally, we investigate the relationship between eventuality and safety synthesis for hybrid automata and reach the conclusion that there is no duality in the extraction of the control law.

Target control for hybrid systems with linear continuous dynamics

We consider the target control problem for hybrid systems with linear continuous dynamics. The system is modelled as a hybrid automaton. Control action is applied on the discrete level, while the continuous dynamics is subject to constant or set valued disturbance. The proposed controller ensures that the system can be transferred from any point of an initial set to a target set of the hybrid state space. A control design algorithm based on reachability analysis is proposed. For the implementation of the algorithm, approximate reachability analysis is employed. This involves under-approximation of reachable sets under linear continuous dynamics. The algorithm is applied to a batch control problem.